A bag contains 6 white and 4 black balls. A die is rolled once and number of balls equal to number o

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14.Probability

medium

A bag contains $6$ white and $4$ black balls. A die is rolled once and the number of balls equal to the number obtained on the die are drawn from the bag at random. The probability that all the balls drawn are white is:

$\frac{1}{4}$

$\frac{9}{50}$

$\frac{1}{5}$

$\frac{11}{50}$

(JEE MAIN-2023)

Solution

$\frac{1}{6} \times\left[\frac{{ }^6 C _1}{{ }^{10} C _1}+\frac{{ }^6 C _2}{{ }^{10} C _2}+\frac{{ }^6 C _3}{{ }^{10} C _3}+\frac{{ }^6 C _4}{{ }^{10} C _4}+\frac{{ }^6 C _5}{{ }^{10} C _5}+\frac{{ }^6 C _6}{{ }^{10} C _6}\right]$

$=\frac{1}{6}\left(\frac{126+70+35+15+5+1}{210}\right)=\frac{42}{210}=\frac{1}{5}$

Standard 11

Mathematics

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normal

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